Looking faster and keener, Murray pushed through the second set in 37 minutes and the third in one minute less.
He dropped further behind the baseline and allowed Kuznetsov to dictate while clapping and grinning sarcastically towards his box.
But a remarkable point early in the second set put him on the right course.
The world number one got past Russian Andrey Kuznetsov in four sets - 6-4 4-6 6-2 6-0. "We will get a good crowd and there will be a great atmosphere". It was quite windy today.
As well as being able to work on the practice court with his team on the days between matches, Murray welcomes the scope that playing over the best of five sets offers.
Klizan - who went on to make 67 unforced errors - threw his racket down after Murray held in the next game, but regained his composure to hold and was a set up after winning a tie-break in which the Wimbledon champion was unhappy with a line call prior to double faulting.
Just 4-4 this clay season and with only one title this year, Andy Murray admits it's been a tough start to 2017. I was hitting the ball better when I was defending.
"Obviously I saw a few videos of his match".
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"I have not had too many bad illnesses. At times I played some very solid stuff". In the victory, Murray won 72 percent of his first serve points and 54 percent of his second serve points.
And a poor game when he was serving for the set was swiftly cancelled out by a break to love.
Kuznetsov, meanwhile, has had a good clay season and made the semi-finals of the Geneva Open last week.
The contest looked like it could go either way but, once Murray took control, he showed the sort of ruthlessness that bodes well for the rest of the tournament.
The Slovakian, ranked No.50, then began to chance his arm and, as Murray's level dipped, raced to a 5-2 lead before, with yet another momentum shift, the Scot broke back and took the fourth set to a tiebreak, closing out the match with a scrambled volley. But I kept fighting.
"It's frustrating - it's the third time I have been ill this year", he admitted. As it went on I hit deeper and started to dictate more points.
"I will get through it - I'm sure of that. I did that in the end".
Murray will face Martin Klizan for a place in the last 32 after the Slovak prevailed in a tense five-setter against French wild card Laurent Lokoli.
The former champion claimed a convincing victory - 6-2 7-6 (8-6) 6-3. "After that, he talks to me of respect".
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